Mathieu, 26, joined the Texans on a one-year, $7 million deal last offseason after he was released by the Arizona Cardinals just before the start of the new NFL year. He had been drafted by Arizona in 2013.
Driven to be "one of the best safeties in this league," Mathieu played in all 16 games for the second consecutive season and tied his career high with 89 tackles. He also had three sacks, a fumble recovery and two interceptions.
Before joining the Texans, Mathieu ended three of his first five NFL seasons on injured reserve. He tore his left ACL and LCL in 2013 and his right ACL in 2015, when he was a first-team All-Pro and selected to the Pro Bowl. In 2017, he played in all 16 games for the first time since entering the NFL.
The Chiefs are intent on finding a safety to pair with Eric Berry, who missed most of last season with a foot injury. Berry carries a massive salary-cap hit, but the Chiefs missed out on Landon Collins in free agency and appear content to keep Berry on the roster.
If Berry is healthy, he and Mathieu would form one of the AFC's best safety duos.
Anything would be an upgrade from last season, when the Chiefs allowed a league-worst 425.6 yards and 35.3 points per game. The defense ultimately let down Kansas City when it mattered most, failing to get off the field in overtime in an AFC title game loss to the New England Patriots.
Defensive coordinator Bob Sutton was fired within days of the loss. The Chiefs quickly hired Steve Spagnuolo, and now they are beginning to piece together what they hope is a vastly improved unit.
"One great thing about Steve is he is going to put players in positions to make plays and I don't think he is going to be pigeonholed into any one idea or concept,'' Chiefs general manager Brett Veach said earlier this month. "We have a great coaching staff. We certainly have some talent on our roster now and hopefully we will add some more here soon.''
ESPN's Sarah Barshop and The Associated Press contributed to this report.